A distinctive feature of Kaluza-Klein compactification [1]}, [2]} of a top theory are infinite towers of fields of increasing masses and decreasing spins in the resulting bottom theory.In this paper, we use the terms top and bottom theories to designate respective higher-dimensional and lower-dimensional theories in the context of the Kaluza-Klein type mechanisms. The same property holds both in the AdS dimensional degression [3]}, [4]} and the AdS waveguide compactification [5]}. In this paper we show that the spectrum of a bottom theory can be finite if one starts with a topological theory in higher-dimensional AdS space. Specifically, we study the AdS\(_{3}\) /AdS\(_2\)  degression for a spin-\(s\)  massless field theory. The resulting AdS\(_2\)  spectrum consists of finitely many propagating modes. To some extent this phenomenon is similar to the Brown-Henneaux relation for \(3d\)  Einstein gravity with the cosmological term without local degrees of freedom which under appropriate AdS\(_3\)  boundary conditions
encoding=*-50leads to \(2d\)  boundary \(\mathbb {R}^2\)  local degrees of freedom spanning Virasoro algebra representations [6]}.
encoding=*0
